Tensor Product for SIR Model (A * X * B')
cpp_tprod_A_X_Bt.RdPerforms the bilinear transformation central to the Social Influence Regression model. Computes A * X_t * B' for each time slice t, where this product represents how network influence flows through the sender effects (A) and receiver effects (B).
Arguments
- X
Three-dimensional array (m x m x T) representing the network state over time. Each slice X[,,t] is the network at time t that carries influence.
- A
Matrix (m x m) of sender effects. Element A[i,k] represents how node i is influenced by the sending behavior of node k.
- B
Matrix (m x m) of receiver effects. Element B[j,l] represents how node j's reception is modified by node l's receiving patterns.
Value
Three-dimensional array (m x m x T) where element [i,j,t] represents the total bilinear influence from node i to node j at time t.
Details
This operation is the computational bottleneck of the SIR model, appearing in both the likelihood evaluation and gradient computation. The function implements:
For each time t: Result[,,t] = A * X[,,t] * B'
Where: - A captures sender-specific influence patterns (how nodes affect others) - B captures receiver-specific influence patterns (how nodes are affected) - X typically contains lagged network outcomes that carry influence forward
Mathematical interpretation: - Element (i,j) of the result represents the total influence flowing from i to j - This influence is mediated by the entire network structure at time t - The bilinear form allows for complex, indirect influence pathways
Computational optimizations: - Pre-computes B' once rather than for each time slice - Uses Armadillo's optimized BLAS routines for matrix multiplication - Memory-efficient slice-wise operations to avoid large temporary matrices - Compiler optimizations enabled through RcppArmadillo