Calculate derivative of mu_i with respect to a row of matrix-valued parameter rho_tilde.

Usage

mu_d_rho_tilde_faster(
  i,
  J,
  k_tilde,
  gammas,
  B,
  rho_tilde_k,
  A_tilde_k_list,
  fixed_P_tilde_multipliers,
  X_tilde,
  Z_tilde,
  Z_tilde_gamma_cols,
  alpha_tilde = NULL,
  Z_tilde_list = NULL,
  gamma_tilde,
  proportion_scale = FALSE
)

Arguments

i: The sample index (must be in 1, ..., n)
J: The total number of taxa modeled
k_tilde: Row index (which row of rho_tilde with respect to which to take derivative)
gammas: Numeric vector of read intensities
B: Detection efficiency matrix
rho_tilde_k: Value of kth row of rho_tilde
A_tilde_k_list: List containing matrices that map back-transformed rho_tilde to entries of P_tilde
fixed_P_tilde_multipliers: Numeric vector of row-specific multipliers applied to the derivative of the transformation from \(\tilde{\rho}\) to \(\tilde{P}\).
X_tilde: The spurious read efficiency design (K_tilde x p)
Z_tilde: The spurious read design (n x K_tilde)
Z_tilde_gamma_cols: Numeric vector containing indexes of columns of Z_tilde to scale by exp(gamma); NULL if no columns to be scaled
alpha_tilde: A numeric vector containing starting values of length \(M\). If used, Z_tilde_list must be provided.
Z_tilde_list: A list of length \(M + 1\) containing matrices \(\tilde{Z}_1,\dots,\tilde{Z}_{M + 1}\) to be linearly combined to generate Z_tilde: \(\tilde{Z} = \tilde{Z}_{(1)} + \sum_{m = 1}^M \exp(\tilde{\alpha}_m)\tilde{Z}_{(m + 1)}\). If used, alpha_tilde must be provided.
gamma_tilde: Numeric vector of row-specific intercept terms for the spurious read model.
proportion_scale: Logical. If FALSE, return the derivative of \(\mu_i\) with respect to row k_tilde of \(\tilde{\rho}\). If TRUE, return only the derivative with respect to the corresponding row of \(\tilde{P}\).

Value

A derivative d mu_i / d rho_tilde_k