Array-Matrix Product for Influence Matrices

Computes a weighted sum of influence covariate matrices to construct the parameterized influence matrices A or B in the SIR model.

Usage

cpp_amprod_W_v(W, v)

Arguments

W: Three-dimensional array (m x m x p) of influence covariates. Each slice W[,,k] represents one way nodes can influence each other (e.g., geographic proximity, social distance, shared attributes).
v: Vector (p x 1) of coefficients for the linear combination. These are the parameters being estimated (either alpha or beta).

Value

Matrix (m x m) representing the weighted combination of influence covariate matrices. This becomes either the A or B matrix in the model.

Details

This function implements the parameterization: Result = sum(k=1 to p) v[k] * W[,,k]

In the SIR model context: - A = sum(k=1 to p) alpha[k] * W[,,k] (alpha[1] = 1 fixed) - B = sum(k=1 to p) beta[k] * W[,,k]

The parameterization reduces the number of free parameters from O(m^2) to O(p), where typically p << m. This makes estimation feasible for larger networks.

Computational strategy: - Skips zero coefficients to save computation - Uses in-place addition to minimize memory allocation - Leverages Armadillo's expression templates for efficiency

Note

The function checks for dimension compatibility and will throw an error if v has incorrect length. Zero coefficients are detected and skipped to improve performance when the model is sparse.