operator.operations: Operations with the Pr and Pl operators

In rSPDE: Rational Approximations of Fractional Stochastic Partial Differential Equations

Operations with the Pr and Pl operators

Description

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.

Value

A vector with the values of the operation

rSPDE documentation built on Nov. 6, 2023, 1:06 a.m.