Package 'nntmvn'

Find ordered nearest neighbors based on correlation, assuming the absolute value of the correlation is monotonically decreasing with distance. Returns an n X (m + 1) matrix, each row indicating the m + 1 nearest neighbors including itself.

Description

Find ordered nearest neighbors based on correlation, assuming the absolute value of the correlation is monotonically decreasing with distance. Returns an n X (m + 1) matrix, each row indicating the m + 1 nearest neighbors including itself.

Usage

corr_nn(covmat, m)

Arguments

covmat	the covariance matrix
m	the number of nearest neighbors

Value

an n X (m + 1) matrix

Examples

library(RANN)
library(nntmvn)
set.seed(123)
d <- 3
n <- 100
locs <- matrix(runif(d * n), n, d)
covparms <- c(2, 0.01, 0)
covmat <- GpGp::matern15_isotropic(covparms, locs)
m <- 10
NNarray_test <- RANN::nn2(locs, k = m + 1)[[1]]
NNarray <- nntmvn::corr_nn(covmat, m)
cat("Number of mismatch is", sum(NNarray != NNarray_test, na.rm = TRUE))

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nntmvn

Description

Draw Samples of Truncated Multivariate Normal Distributions

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Draw one sample of the underlying GP responses for a partially censored Gaussian process using sequential nearest neighbor (SNN) method

Description

Draw one sample of the underlying GP responses for a partially censored Gaussian process using sequential nearest neighbor (SNN) method

Usage

rptmvn(
  y,
  cens_lb,
  cens_ub,
  mask_cens,
  m = 30,
  covmat = NULL,
  locs = NULL,
  cov_name = NULL,
  cov_parm = NULL,
  NN = NULL,
  ordering = 0,
  seed = NULL
)

Arguments

y	uncensored responses of length n, where n is the number of all responses
cens_lb	lower bound vector for TMVN of length n
cens_ub	upper bound vector for TMVN of length n
mask_cens	mask for censored responses (also locations) of length n
m	positive integer for the number of nearest neighbors used
covmat	n-by-n dense covariance matrix, either covmat or locs, cov_name, and cov_parms need to be provided
locs	location matrix n X d
cov_name	covariance function name from the GpGp package
cov_parm	parameters for the covariance function from the GpGp package
NN	n X m matrix for nearest neighbors. i-th row is the nearest neighbor indices of y_i. NN[i, 1] should be i
ordering	0 for do not reorder, 1 for variance descending order, 2 for maximin ordering
seed	set seed for reproducibility

Value

a vector of length n representing the underlying GP responses

Examples

library(GpGp)
library(RANN)
library(nntmvn)
set.seed(123)
x <- matrix(seq(from = 0, to = 1, length.out = 51), ncol = 1)
cov_name <- "matern15_isotropic"
cov_parm <- c(1.0, 0.1, 0.001) #' variance, range, nugget
cov_func <- getFromNamespace(cov_name, "GpGp")
covmat <- cov_func(cov_parm, x)
y <- t(chol(covmat)) %*% rnorm(length(x))
mask <- y < 0.3
y_cens <- y
y_cens[mask] <- NA
lb <- rep(-Inf, 100)
ub <- rep(0.3, 100)
m <- 10
y_samp_mtd1 <- rptmvn(y_cens, lb, ub, mask,
  m = m, locs = x,
  cov_name = cov_name, cov_parm = cov_parm, seed = 123
)
y_samp_mtd2 <- rptmvn(y_cens, lb, ub, mask,
  m = m, covmat = covmat,
  seed = 123
)
plot(x, y_cens, ylim = range(y))
points(x[mask, ], y[mask], col = "blue")
plot(x, y_cens, ylim = range(y))
points(x[mask, ], y_samp_mtd1[mask], col = "red")
plot(x, y_cens, ylim = range(y))
points(x[mask, ], y_samp_mtd2[mask], col = "brown")

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Draw one sample from a truncated multivariate normal (TMVN) distribution using sequential nearest neighbor (SNN) method

Description

Draw one sample from a truncated multivariate normal (TMVN) distribution using sequential nearest neighbor (SNN) method

Usage

rtmvn(
  cens_lb,
  cens_ub,
  m = 30,
  covmat = NULL,
  locs = NULL,
  cov_name = NULL,
  cov_parm = NULL,
  NN = NULL,
  ordering = 0,
  seed = NULL
)

Arguments

cens_lb	lower bound vector for TMVN of length n
cens_ub	upper bound vector for TMVN of length n
m	positive integer for the number of nearest neighbors used
covmat	n-by-n dense covariance matrix, either covmat or locs, cov_name, and cov_parms need to be provided
locs	location matrix n X d
cov_name	covariance function name from the GpGp package
cov_parm	parameters for the covariance function from the GpGp package
NN	n X m matrix for nearest neighbors. i-th row is the nearest neighbor indices of y_i. NN[i, 1] should be i
ordering	0 for do not reorder, 1 for variance descending order, 2 for maximin ordering
seed	set seed for reproducibility

Value

a vector of length n representing the underlying GP responses

Examples

library(nntmvn)
library(TruncatedNormal)
set.seed(123)
x <- matrix(seq(from = 0, to = 1, length.out = 51), ncol = 1)
cov_name <- "matern15_isotropic"
cov_parm <- c(1.0, 0.1, 0.001) #'' variance, range, nugget
cov_func <- getFromNamespace(cov_name, "GpGp")
covmat <- cov_func(cov_parm, x)
lb <- rep(-Inf, nrow(x))
ub <- rep(-1, nrow(x))
m <- 30
samp_SNN <- matrix(NA, 3, nrow(x))
for (i in 1:3) {
  samp_SNN[i, ] <- nntmvn::rtmvn(lb, ub, m = m, covmat = covmat, locs = x, ordering = 0)
}
samp_TN <- TruncatedNormal::rtmvnorm(3, rep(0, nrow(x)), covmat, lb, ub)
qqplot(samp_SNN, samp_TN, xlim = range(samp_SNN, samp_TN), ylim = range(samp_SNN, samp_TN))
abline(a = 0, b = 1, lty = "dashed", col = "red")

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