Description Usage Arguments Details Value See Also Examples
View source: R/spacetime_bisquare.R
Spacetime bisquare basis on point data.
1  spacetime_bisquare(dom, knots, w_s, w_t)

dom 
Spacetime points (\bm{u}_1,v_1), …, (\bm{u}_n,v_n) to evaluate. See "Details". 
knots 
Spatiotemporal knots (\bm{c}_1,g_1), …, (\bm{c}_r,g_r) for the basis. See "Details". 
w_s 
Spatial radius for the basis. 
w_t 
Temporal radius for the basis. 
Notes about arguments:
Both dom
and knots
may be provided as either sf
or
sfc
objects, or as matrices of points.
If an sf
or sfc
object is provided for dom
, n
threedimensional POINT
entries are expected in st_geometry(dom)
.
Otherwise, dom
will be interpreted as an n \times 3 numeric matrix.
If an sf
or sfc
object is provided for knots
, r
threedimensional POINT
entries are expected in st_geometry(knots)
.
Otherwise, knots
will be interpreted as an r \times 3 numeric matrix.
If both dom
and knots_s
are given as sf
or sfc
objects,
they will be checked to ensure a common coordinate system.
For each (\bm{u}_i,v_i), compute the basis functions
ψ_j(\bm{u},v) = ≤ft[ 2  \frac{\Vert \bm{u}  \bm{c}_j \Vert^2}{w_s^2} \frac{v  g_j^2}{w_t^2} \right]^2 \cdot I(\Vert \bm{u}  \bm{c}_j \Vert ≤q w_s) \cdot I(v  g_j ≤q w_t)
for j = 1, …, r.
Due to the treatment of \bm{u}_i and \bm{c}_j as points in a Euclidean space, this basis is more suitable for coordinates from a map projection than coordinates based on a globe representation.
A sparse n \times r matrix whose ith row is
\bm{s}_i^\top = \Big( ψ_1(\bm{u}_i,v_i), …, ψ_r(\bm{u}_i,v_i) \Big).
Other bisquare:
areal_spacetime_bisquare()
,
areal_spatial_bisquare()
,
spatial_bisquare()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  set.seed(1234)
# Create knot points
seq_x = seq(0, 1, length.out = 3)
seq_y = seq(0, 1, length.out = 3)
seq_t = seq(0, 1, length.out = 3)
knots = expand.grid(x = seq_x, y = seq_y, t = seq_t)
knots_sf = st_as_sf(knots, coords = c("x","y","t"), crs = NA, dim = "XYM", agr = "constant")
# Points to evaluate
x = runif(50)
y = runif(50)
t = sample(1:3, size = 50, replace = TRUE)
pts = data.frame(x = x, y = y, t = t)
dom = st_as_sf(pts, coords = c("x","y","t"), crs = NA, dim = "XYM", agr = "constant")
rad = 0.5
spacetime_bisquare(cbind(x,y,t), knots, w_s = rad, w_t = 1)
spacetime_bisquare(dom, knots_sf, w_s = rad, w_t = 1)
# Plot the (spatial) knots and the points at which we evaluated the basis
plot(knots[,1], knots[,2], pch = 4, cex = 1.5, col = "red")
text(x, y, labels = t, cex = 0.75)
# Draw a circle representing the basis' radius around one of the knot points
tseq = seq(0, 2*pi, length=100)
coords = cbind(rad * cos(tseq) + seq_x[2], rad * sin(tseq) + seq_y[2])
lines(coords, col = "red")

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