C_Q: Active subspace for second order linear model

In activegp: Gaussian Process Based Design and Analysis for the Active Subspace Method

Active subspace for second order linear model

Description

Active subspace for second order linear model

Usage

C_Q(design, response)

Arguments

design	A matrix of design points, one in each row, in [-1,1]^d
response	A vector of observations at each design point.

Value

A matrix corresponding to the active subspace C matrix.

Examples

set.seed(42) 
A <- matrix(c(1, -1, 0, -1, 2, -1.5, 0, -1.5, 4), nrow = 3, byrow = TRUE)
b <- c(1, 4, 9)

# Quadratic function
ftest <- function(x, sd = 1e-6){
   if(is.null(dim(x))) x <- matrix(x, nrow = 1)
   return(3 + drop(diag(x %*% A %*% t(x)) + x %*% b) + 
     rnorm(nrow(x), sd = sd))
}

ntrain <- 10000
design <- 2 * matrix(runif(ntrain * 3), ntrain) - 1
response <- ftest(design)

C_hat <- C_Q(design, response)

plot(design %*% eigen(C_hat)$vectors[,1], response)

# Test 
gfun <- function(x){2 * A %*% t(x) + matrix(b, nrow = nrow(A), ncol = nrow(x))}
grads <- gfun(design)
C_MC <- tcrossprod(grads)/ntrain
C_true <- 4/3 * A %*% A + tcrossprod(b)
subspace_dist(eigen(C_MC)$vectors[,1:2], eigen(C_true)$vectors[,1:2]) 

activegp documentation built on June 28, 2022, 1:05 a.m.