Functions for multiplying and solving with the \(P_r\) and \(P_l\) operators as well as the latent precision matrix \(Q = P_l C^{-1}P_l\) and covariance matrix \(\Sigma = P_r Q^{-1} P_r^T\). These operations are done without first assembling \(P_r\), \(P_l\) in order to avoid numerical problems caused by ill-conditioned matrices.
Usage
Pr.mult(obj, v, transpose = FALSE)
Pr.solve(obj, v, transpose = FALSE)
Pl.mult(obj, v, transpose = FALSE)
Pl.solve(obj, v, transpose = FALSE)
Q.mult(obj, v)
Q.solve(obj, v)
Qsqrt.mult(obj, v, transpose = FALSE)
Qsqrt.solve(obj, v, transpose = FALSE)
Sigma.mult(obj, v)
Sigma.solve(obj, v)Arguments
- obj
rSPDE object
- v
vector to apply the operation to
- transpose
set to TRUE if the operation should be performed with the transposed object
Details
Pl.mult, Pr.mult, and Q.mult
multiplies the vector with the respective object.
Changing mult to solve in the function names
multiplies the vector with the inverse of the object.
Qsqrt.mult and Qsqrt.solve performs the
operations with the square-root type object
\(Q_r = C^{-1/2}P_l\) defined so that \(Q = Q_r^T Q_r\).