## S3 method for class 'mgram'
residuals(object, ...)

#### Partial pmgram example

# generate a simple surface
# with complex nonlinear spatial pattern

x <- matrix(1:10, nrow=10, ncol=10, byrow=FALSE)
y <- matrix(1:10, nrow=10, ncol=10, byrow=TRUE)

# create z1 and z2 as functions of x, y
# and scale them to [0, 1]
z1 <- x + 3*y
z2 <- y - cos(x)

z1 <- (z1 - min(z1)) / (max(z1) - min(z1))
z2 <- (z2 - min(z2)) / (max(z2) - min(z2))

z12 <- (z1 + z2*2)/3

# analyze the pattern of z across space
z1 <- as.vector(z1)
z2 <- as.vector(z2)
z12 <- as.vector(z12)
z1.d <- dist(z1)
z2.d <- dist(z2)
z12.d <- dist(z12)

space <- cbind(as.vector(x), as.vector(y))
space.d <- dist(space)

# take partial correlogram of z12 given z1
z.z1 <- pmgram(z12.d, space.d, z2.d, nperm=0, resids=TRUE)
summary(residuals(z.z1))