rSPDE.A1d {rSPDE}

Observation matrix for finite element discretization on R

Description

A finite element discretization on R can be written as u(s) = \sum_i^n u_i \varphi_i(s) where \varphi_i(s) is a piecewise linear "hat function" centered at location x_i. This function computes an m\times n matrix A that links the basis function in the expansion to specified locations s = (s_1,\ldots, s_m) in the domain through A_ij = \varphi_j(s_i).

Usage

rSPDE.A1d(x, loc)

Arguments

x

The locations of the nodes in the FEM discretization.

loc

The locations (s_1,\ldots, s_m)

Value

The sparse matrix A.

Author(s)

David Bolin [e-mail]

See Also

rSPDE.fem1d()

Examples

# create mass and stiffness matrices for a FEM discretization on [0,1]
x <- seq(from = 0, to = 1, length.out = 101)
fem <- rSPDE.fem1d(x)

# create the observation matrix for some locations in the domain
obs.loc <- runif(n = 10, min = 0, max = 1)
A <- rSPDE.A1d(x, obs.loc)