# Linv_mult: Multiply approximate inverse Cholesky by a vector In GpGp: Fast Gaussian Process Computation Using Vecchia's Approximation

## Description

Vecchia's approximation implies a sparse approximation to the inverse Cholesky factor of the covariance matrix. This function returns the result of multiplying that matrix by a vector.

## Usage

 `1` ```Linv_mult(Linv, z, NNarray) ```

## Arguments

 `Linv` Entries of the sparse inverse Cholesky factor, usually the output from `vecchia_Linv`. `z` the vector to be multiplied `NNarray` A matrix of indices, usually the output from `find_ordered_nn`. Row `i` contains the indices of the observations that observation `i` conditions on. By convention, the first element of row `i` is `i`.

## Value

the product of the sparse inverse Cholesky factor with a vector

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```n <- 2000 locs <- matrix( runif(2*n), n, 2 ) covparms <- c(2, 0.2, 0.75, 0.1) ord <- order_maxmin(locs) NNarray <- find_ordered_nn(locs,20) Linv <- vecchia_Linv( covparms, "matern_isotropic", locs, NNarray ) z1 <- rnorm(n) y <- fast_Gp_sim_Linv(Linv,NNarray,z1) z2 <- Linv_mult(Linv, y, NNarray) print( sum( (z1-z2)^2 ) ) ```

GpGp documentation built on June 10, 2021, 1:07 a.m.