### Name: conv.gp
### Title: Gaussian process modeling via Spatial Convolutions
### Aliases: conv.gp.1d conv.gp.2d conv.gp.multi.1d conv.gp.multi.2d
###   conv.gp.mc.1d
### Keywords: models spatial

### ** Examples

# -------------------------
# ONE dimensional synthetic  data
# --------------------------------

# get the synthetic data
data <- data.1d()
pdata <- seq(1,10,length=100)

# -----------------------
# SINGLE Resolution model
# -----------------------

# centers of the kernels (must be a matrix)
w <- as.matrix(seq(1-2,10+2,length=7))

# prepare the 1-d ML convolution model
data.conv.gp <- conv.gp.1d(data, pdata=pdata, w=w, sdkern=2)

# plot the results
plot(data.conv.gp, main="1-d Single Resolution")

# ----------------------
# MULTI Resolution model
# ----------------------

# kernels: number of support points at each scale
m1 <- c(7,14,28) 

# kernel centers: list to hold the support locations
w1 <- list()  # (must be a list)
for(i in 1:3) w1[[i]] <- seq(1-2,10+2,length=m1[i])

# kernels: width by scale
sdkern <- c(2,1,.5)

# estimate the 1-d ML convolution model
data.conv.gp.multi <- conv.gp.multi.1d(data, pdata=seq(1,10,length=100), w=w1, sdkern=sdkern)

# plot the results
plot(data.conv.gp.multi, main="1-d Multiple Resolution")

# ___________________________________________________________________________
# ___________________________________________________________________________
#

# ---------------------------
# TWO dimensional ozone data
# ---------------------------

# get the 2d ozone data
ozone <- data.ozone()
x <- ozone$s[,1]; y <- ozone$s[,2]
pdata <- as.matrix(grid.2d(x,y,20,20))

# -----------------------
# SINGLE Resolution model
# -----------------------

# locations of support points w (must be a matrix)
wrows <- 6; wcols <- 8
w <- as.matrix(grid.2d(x,y,wrows,wcols))

# width of kernel
sdkern <- 2*diag(1,2,2)

# prepare the 2-d ML convolution model
ozone.conv.gp <- conv.gp.2d(ozone, pdata=pdata, w=w, sdkern=sdkern)

# plot the results
plot(ozone.conv.gp, main="2-d Ozone")

# -------------------------
# MULTIPLE Resolution model
# -------------------------

# make support locations w (must be a list)
w <- list( sparce=grid.2d(x,y,4,5), med=grid.2d(x,y,6,8), fine=grid.2d(x,y,9,12))

# width of the kernels
sdkern <- list( sparce=2*diag(1,2,2), med=1*diag(1,2,2), fine=0.5*diag(1,2,2))

# estimate the 2-d ML convolution model
ozone.conv.gp.multi <- conv.gp.multi.2d(ozone, pdata=pdata, w=w, sdkern=sdkern)

# plot the results
plot(ozone.conv.gp.multi, main="2-d Ozone Multi")